A photograph taken on a mobile phone shows an Isis flag in front of the provincial government headquarters in Mosul this week. Naqshbandi militants are said to have removed many such flags. Photograph: AP

Isis fighters have partially withdrawn from Iraq's second city, Mosul, where another militant group - closely linked to former members of Saddam Hussein's regime - has taken over large areas, according to the city's governor.

In an interview with the Guardian the governor, Atheel Nujaifi, who escaped from Mosul last month, said the Islamic State's main "strike force" had withdrawn from the city to fight the Iraqi army further south in Tikrit, he said. A smaller number of local Isis supporters remained in Mosul's western part, known as the right bank, he said.

Last month Isis staged a stunning advance, seizing Mosul and Tikrit, and raising the spectre of Iraq's collapse. On Tuesday the Iraqi army was forced to retreat from Tikrit, Saddam Hussein's birthplace, 100 miles north of Baghdad, after its latest attempt to retake the city met heavy Isis resistance.

Izzat Ibrahim al-Douri, the king of clubs according to the US defence department Photograph: US Department Of Defense/EPA

But according to Nujaifi, most of the eastern half of Mosul is now dominated by the Naqshbandi Army, a group led by high-ranking Saddam-era Ba'athists including Izzat al-Douri, the king of clubs in the US deck of "wanted Iraqi" playing cards. Naqshbandi militants had taken down Isis flags from "a lot of buildings" and replaced them with their own, he said. Other sources inside Mosul confirmed that Isis fighters began to withdraw from the city about a week ago.

The lightning Isis offensive, which swept Iraqi government forces from swaths of the country's north, is thought to have been partially enabled by an alliance with the Naqshbandi group - known in full as the Army of the Men of the Naqshbandi Order which emerged around 2007. The group is believed to be under the control of Douri, the most senior of Saddam's commanders to evade capture after the 2003 US-led invasion of Iraq. His whereabouts is unknown, though many think he is in Syria.

"They [the Naqshbandi group] have a direct relationship with al-Douri," the governor said. "It's a Sufi group. Al-Douri is himself a Sufi."

Nujaifi said the only way out of Iraq's current violent turmoil was a political solution involving talks not with Isis but with the "six or seven" other Sunni groups fighting in different parts of the country. All are opposed to Iraq's Shia-led government, and its prime minister, Nouri al-Maliki. "The solution must be without Maliki. Nobody trusts him," the governor said.

Residents in Mosul, meanwhile, say Iraqi aircraft are regularly bombarding the city, and on Tuesday night hit its main power plant, next to Mosul University. Water supplies have already been cut. Electricity – previously available for a couple of hours a day – is now down to just a few minutes, forcing people to rely on generators. Prices for basic foodstuffs and petrol have risen dramatically.

The northern city of around two million is by far the biggest to have fallen into the hands of Isis. When jihadi fighters swept into Mosul on 10 June, many initially welcomed their arrival: the city is predominantly Sunni, and the Shia-dominated Baghdad government and its local police force in Mosul were deeply unpopular. Locals described how Isis militants attempted to win over locals, using army cranes to remove Mosul's numerous checkpoints, for example. One shopkeeper said that before the militants' arrival it had taken one hour to cross the city; now it took just 15 minutes.

One resident said most Isis fighters had vanished late last week. They were now largely invisible, with only a few low-key checkpoints inside the city. "They left their houses. You only see them now in on patrol at night, a couple of cars. Before in the same neighbourhoods I saw hundreds of fighters celebrating their victory," the resident said.

So far, there has been no conflict between the Naqshbandi Army and Isis, who are now facing off in Mosul on opposite banks of the Tigris river. But the governor said that a struggle was inevitable. "Logically, they will confront each other," he said. Local Sunni factions in several Iraqi provinces were stronger than Isis, he added. The faultline was between "nationalist" groups and hardline Salafist outfits, he said, which had emerged from a rigid "ideological, Islamic background".

Nujaifi said he reluctantly left Mosul on the advice of his security officers on 10 June, as the Iraqi army fled. He initially stayed at his farm outside the city, but left that too as Isis rolled forward.

His son Abdullah said Isis had stolen the family's 200 pure breed Arab horses, adding: "One third of them will be dead by now."

The governor hinted there could be a deal over control of Mosul in the near future. "With Naqshbandi it's easier to get a solution," he said. "The ideological people [from Isis] aren't interested in the city. They've left."

For the moment, though, Isis militants are killing about five or six people a day, the governor said, citing sources inside the city's mortuary.

The governor said he believed the man who appeared in a video making a speech from Mosul's al-Nuri mosque on 5 July was indeed Abu Bakr al-Baghdadi, Isis's leader. In the footage, Baghdadi proclaimed a new Islamic caliphate stretching from Iraq to Syria, with himself as its ruler. "I think he is a simple man," the governor said. "It wasn't a high-level speech."

Nujaifi said the choice of the 900-year-old mosque, known for its wonky minaret, and elaborate brickwork, was deliberate. It evoked a historical war against the Shia, he said: in the 12th century Nur al-Din set off from the mosque to defeat the Shia Fatamid caliphate in Cairo.

One former Saddam-era general, now in Kurdish Irbil, said he had shared a cell with Baghdadi back in 2004. Both were imprisoned by the Americans in Abu Ghraib, in camp C, just outside Baghdad, he said. The general said the prison become a training school for Sunni militants who would go on to take part in the growing insurgency against US forces. "I would give lectures on special forces training," he said wryly.

He described Baghdadi as an "average guy". "He was a normal fighter, one of thousands who fought the Americans. He smoked a lot. Strange to think he is now leading Isis."

Mohammad Moslawi is the pseudonym of an Iraqi journalist working in Mosul